I was solving a math problem and the book at some point wrote that
$$\gcd(44m+15;15m+5) = \gcd(m;5)$$ when $m$ is an integer.
Why?
2026-04-09 02:04:47.1775700287
Why is $\gcd(44m+15;15m+5) = \gcd(m;5)$?
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$$\gcd(44m+15, 15m+5)=\gcd(-m,15m+5)=\gcd(-m, 5)=\gcd(m,5)$$
The first equalities derive from the property of the gcd that states: $\gcd(n,m)=\gcd(n-km, m)$, where $k$ is an integer. The last equality is trivial since the divisors of $m$ are the same as the divisors of $-m$.